A monoatomic ideal gas, initially at temperature `T_1,` is enclosed in a cylinder fitted with a friction less piston. The gas is allowed to expand adiabatically to a temperature `T_2` by releasing the piston suddenly. If `L_1 and L_2` are the length of the gas column before expansion respectively, then `(T_1)/(T_2)` is given by

Options

A. (a) `((L_1)/(L_2))^(2/3)`
B. (b) `L_1/L_2`
C. (c) `L_2/L_1`
D. (d) `((L_2)/(L_1))^(2/3)`

Answer

D

Explanation

`TV^(gamma-1)=`constant
`:.` `T_1/T_2=(V_2/V_1)^(gamma-1)`
`=(L_2/L_1)^(5//3-1)=(L_2/L_1)^(2//3)`